Calculus for Tan Gents, and Other Unwritten Math Books

Usually, my sons are my best audience.

Several nights ago, as we were having dinner with a neighbor and his kids, we started talking about cherries. (I have no idea why.) But not willing to let an opportunity slip away, I offered, “I have a friend named Merah (pronounced mare-ruh) who works in an ice cream shop, and her job is to place cherries on top of sundaes.”

My neighbor looked at me funny. Then he saw where I was going. “Is her last name Sheeno?” he asked.

“It sure is! Merah Sheeno!”

Nothing. Not even the slightest hint of recognition from the boys or from either of my neighbors’ kids.

But I was not deterred. “And she has a brother named Whatduzz.”

Everyone looked at me blankly.

“Whatduzz Sheeno! Get it? ‘What does she know?””

My neighbor nearly fell off his chair. “Oh, that’s good!” he said. “I hadn’t heard that one before.”

“That’s because I just made it up, Hunter.”

“No wonder your sons say you’re the funniest man they know!”

It’s true. That’s what my sons usually say. But not that night. That night, they just thought I was weird.

Someday, I hope to use my ability to make up funny names to write a bestseller under a pseudonym. (At this point, putting my real name on a book would surely lead to negative sales.) Some of my ideas are:

• Putting the Pieces Together, by Lois Carmen Denominator
• Step by Step, by Al Gorithm
• The Longest Side, by Hy Potenuse
• Much Ado About Nothing, by Zee Row
• Big Wheels Keep On Turning, by Cy Cloyd
• Calculus for Tan Gents, by Anne T. Derivative
• Nothing to See Here, by M. T. Set
• Mirror, Mirror, by Reif Lection
• Below the Line, by Dee Nominator
• Can’t Tell Up from Down, by Vin Q. Lum
• Pushing My Buttons, by Cal Culator
• Petal to the Metal, by Rose Curve
• I Lost My Parrot, by Polly Gon
• Three Dimensions, by Polly Hedron
• What My x Got in the Break-Up, by Al Jabra
• Less Than That, by Lisa Perbound
• Local Extremes, by Max Imum and Minnie Mum
• Out In Front, by Lee Ding Coefficient

If some of those names look familiar, you may have seen them in Mathy Names. Thanks to Jim Maher, who contributed some of the names in a comment.

How Much Does Your Name Cost?

Here’s a contrived yet fun math problem that I shared with my sons recently:

A local hardware store sells bronze letters. However, the letters vary in price; some are more expensive than others. When I was at the store the other day, four people purchased the letters in their names. Their names and the prices they paid were:

Aiden $491  •  Ned $225  •  Dane $399  •  Ed $135

The price of a name is equal to the sum of the prices of its letters. The price for uppercase and lowercase letters is the same, and there is no additional surcharge or tax. How much would the following people pay to buy the letters in their names?

Edna  •  Ian  •  Nadine

Those of you who know a little algebra will have no trouble with that problem. Those of you who don’t shouldn’t have too much trouble, either.

But then, I realized I could extend the problem for some added fun. And who am I to keep fun things to myself? So, here ya go.

I saw this sign in a window the other day:

At first, I thought the store was engaging in human trafficking. But then I realized that $269 was the price for the bronze letters that had been used to spell the name Eli. Inside the store was a price list for other names:

AIDEN – 491	AL – 248	ART – 267	BEA – 290
EARL – 415	DANE – 399	ED – 135	ELI – 269
FAY – 220	GABI – 289	HAL – 284	IVY – 143
JACK – 234	JAY – 232	KO – 60	KAI – 283
LEXI – 272	MAVIS – 363	MAX – 215	NED – 225
PAT – 210	PERRI – 330	QI – 93	QUIN – 199
SAMMY – 338	WILL – 243	ZENO – 243

The store didn’t have a list of prices for the individual letters, but then I realized that I didn’t need one. From the table above, I could figure out how much my name  would cost.

Can you figure out how much your name would cost?

You can download both of these problems for use in a classroom (or at a mathy party) from the following link:

Name Letters (PDF)

And while I don’t believe in answer keys, you can check your work by using the form found on this page.

Name Letter Form

For what it’s worth, the longest name ever — according to Wolfe + 585, Senior, who has a pretty long name himself — is Rhoshandiatellyneshiaunneveshenk Koyaanisquatsiuth Williams. Her entire name name would have cost $4,073 at this store — an astounding $2,359 for her first name, $1,119 for her middle name, and a veritable bargain at $595 for her tame-by-comparison last name. (Incidentally, this is the name that appeared on her birth certificate. As the story goes, her father later increased her first name to 1,019 letters and added an additional 36 letters to her middle name. You know… just in case the name wasn’t long or unique enough already.)

Math Name Scramble

When you scramble the letters of “Math Name Scramble,” several excellent anagram-cum-headlines are formed. The results are just too spectacular not to have a little fun.

Lambs Cheat Merman
Schenectady, New York – Maybe she’s got rhythm, but Ethel Merman appears to be lacking in street smarts. When three young, corrupt sheep tempted her with a game of three-card monte, she should have politely declined. But she was insistent that identifying the proper card “shouldn’t be that difficult.” Fourteen failed attempts and $650 later, she finally accepted defeat. The ovine dealer, amused by Ms. Merman’s persistence, continually told her, “I get a kick out of you.”

Math, Camels, Barmen
Riyadh, Saudi Arabia – A mathematician and a camel walk into a bar. The barman says, “What is this, some kind of joke?”

Okay, enough of that silliness.

Lots of math words have interesting anagrams:

• scalene = cleanse
• thousand = handouts
• vector = covert
• algorithm = logarithm
• decimal point = I’m a pencil dot
• integral calculus = calculating rules
• innumerable = a number line

If you like anagrams, the following puzzle might be right up your alley.

The last names of ten famous mathematicians — all sufficiently scrambled, of course — are listed below.

• ACORN PIE
• A PASTRY HOG
• ASS REWRITES
• NO NUN MAVEN
• ON THREE
• RAIN MEN
• REAL GANG
• RED CHAMISE
• SCAREDEST
• THICK NERD EGO

Your task is to unscramble the names, then place them in the rows of the grid below. If you place the correct names in the correct order, another famous mathematician’s name will appear in the highlighted column.

Stumped? Don’t sweat it; lesser men have had to look at the solution, too.

Blog Interview @ www.mathblogging.org

If you’d like to know more about me and this blog — and let’s be honest, why wouldn’t you? — check out my blog interview at mathblogging.org – The Blog. It’s part of their Mathematical Instruments series, in which they interview bloggers whose blogs are listed at www.mathblogging.org. There you can find answers to such burning questions as:

• How did this blog get its name?
• Is my wife smarter than I am?
• What does the internet need more (and less) of?
• What are my favorite blogs?

Addditional info about me and this blog can be found on the About page.

And if that still doesn’t satisfy the information hound in you, feel free to post other questions in the Comments. All tasteful questions will be answered immediately; tasteless questions will be answered as soon as I formulate a witty response.

Dave is a Four-Letter Word

Q: What are these?

• EA + EA + EA + EA + EA + …
• EA + EA + EA + EA + EA + …
• EA + EA + EA + EA + EA + …
• EA + EA + EA + EA + EA + …

A: Four E A series.

I was reminded of this joke when I received a holiday card from my friend DAVE. His wife is ANNE, his daughter is LENA, and his son is AXEL. It struck me as interesting that all four names in their family (1) consist of four letters and (2) contain the letters E and A. That led me to create the following puzzle for my sons.

Can you find a name that fits each of the following patterns?

A __ __ E		A __ E __		A E __ __
__ A __ E		__ A E __		E A __ __
__ __ A E		__ E A __		E __ A __
__ __ E A		__ E __ A		E __ __ A

I was able to complete 75% of the puzzle on my own, and I was able to complete 100% of it with some help from Google. No doubt — the one with AE in the third and fourth positions was the toughest. Good luck!

Incidentally, comedian Penn Jillette (of Penn & Teller) believes the names Dave (my friend) and Alex (my son) were for losers.

What (Math) is in a Name?

One of my favorite online tools is the Mean and Median app from Illuminations. This tool allows you to create a data set with up to 15 elements, plot them on a number line, investigate the mean and median, and consider a box-and-whisker plot based on the data. Perhaps the coolest feature is that you can copy an entire set of data, make some changes, and compare the modified set to the original set. For example, the box-and-whisker plots below look very different, even though the mean and median of the two sets are the same.

It’s a neat tool for learning about mean and median, and I plan to use this tool in an upcoming presentation.

• Exceptional, Free Online Resources for the Middle Grades Classroom
  G. Patrick Vennebush
  Thursday, October 20, 12:30-2:00pm
  Room 401 (Atlantic City Convention Center)

For classroom use, I like to use this app with real sets of data. However, the app requires all elements of a data set to be integers from 1-100. Can you think of a data set with a reasonable spread that has no (or at least few) elements greater than 100? If so, leave a comment.

Recently, and rather accidentally, I found a data set that works well. Do the following:

Assign each letter of the alphabet a value as follows: A = 1, B = 2, C = 3, and so on. Find the sum of the letters in your name; e.g., BOB → 2 + 15 + 2 = 19.

Now imagine that every student in a class finds the sum of the letters in their first name. For a typical class, what is the range of the data? What is the mean and median?

The name with the smallest sum that I could find?

ABE → 1 + 2 + 5 = 8

The name with the largest sum?

CHRISTOPHER → 3 + 8 + 18 + 9 + 19 + 20 + 15 + 16 + 8 + 5 + 18 = 139

The Social Security Administration provides a nice resource for investigation, Popular Baby Names. Using a randomly selected set of 2,000 names and an Excel spreadsheet, I found the mean name sum to be 62.49, and 96% of the names had sums less than 100. Of the 80 names with sums greater than 100, many (such as Christopher, Timothy, Gwendolyn, Jacquelyn) have shortened forms (Chris, Tim, Gwen, Jackie) for which the sum is less than 100.

As it turns out, the frequency with which letters occur in first names differs from their frequency in common English words. The most common letter in English words is e, but the most common letter in names is a. The chart below shows the frequency with which letters occur in first names.

Because of this distribution, the average value of a letter within a first name is 10.54, which is slightly less than the 13.50 you might expect. This is because letters at the beginning of the alphabet, which contribute smaller values to the name sum, occur more often in names than letters at the end of the alphabet.

The chart below shows the distribution for the number of letters within first names. The mean number of letters within first names is 5.92 letters, and the median is 6. (In the data set of 2,000 names from which this chart is derived, no name contained more than 11 letters.)

Do you know a name that has more than 11 letters or has a name sum greater than 139 or less than 8? Let me know in the comments.

Plainly Stated

One of my favorite applets at Illuminations is the State Data Map, which allowed me to create the following map depicting the number of U.S. Presidents born in each state:

Note that the states are color‑coded. Those states in which the greatest number of Presidents were born are the darkest shade of red; those in which no Presidents were born are white. In addition to allowing you to enter data, there are also pre‑loaded data sets. My favorite is the “Letters in State Name” set, from which I concocted the following trivia questions:

• Which state names have the most letters?
• Which state names have the fewest letters?

Feel free to think about it a few seconds before reading the next paragraph.

As it turns out, there are three states whose names contain 13 letters, and there are three states whose names have 4 letters. For what it’s worth, the mean number of letters is 8.24, and the median is 8.

My sons have a collection of foam letters for the bath tub. When the letters get wet, they stick to the side of the tub, and Alex and Eli love to use the letters to spell the names of states. Tonight, Eli spelled WYOMING. We then played a game where I’d give them the name of a state, and they’d try to spell it — but they couldn’t spell many of the state names because the set contains only one copy of each letter of the alphabet. This led to the following trivia question: 

• Which states have names that can be spelled with bath tub letters, i.e., the state name contains no repeated letters?

Feel free to cogitate on that a while, too, then read on.

There are nine states with no repeated letters in their names. (Don’t feel bad if you weren’t able to identify all of them. I had to look at a map.)

Finally, here is a state trivia question a pro pos of absolutely nothing. For each pair of states below, identify the only state that borders both of them. (Each question has a unique answer.)

1. North Carolina, South Carolina
2. South Dakota, Illinois
3. New Mexico, Missouri
4. Oregon, Wyoming
5. Missouri, West Virginia
6. Wisconsin, Ohio

For the answers to all questions, check a map.

What’s in a Name?

The product value of a word can be calculated as follows:

Assign each letter of the alphabet a value as follows: A = 1, B = 2, C = 3, and so on. The product value of a word is the product of its letters. For instance, the word CAT has a product value of 60 because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

During a recent webinar, I introduced participants to my collection of Product Value Puzzles. The following product value puzzle is credited to John Horton Conway:

Find an English word with a product value of 3,000,000.

Finding the solution is up to you. But I will give you some good news — there’s not a unique answer. In fact, there are two English words that satisfy the conditions of the problem.

What most folks found interesting, though, are the Product Value Calculators on my web site. With these two tools, you can:

1. Enter an integer value, and the first calculator will return all words in the English language whose product value equals the number you enter.
2. Enter a word, and the second calculator will return the product value.

One of the participants during the webinar said that her middle school students, when confronted with any type of math puzzle involving words, will first apply the rules of the puzzle to their name. Apparently, I’m not much different from a middle school kid, because that’s what I did, too. Turns out, my name has a product value of 1,710,720:

Patrick = 16 × 1 × 20 × 18 × 9 × 3 × 11 = 1,710,720

So, then I wondered, “Are there any other words that have a product value of 1,710,720?” Of course, I could have used the Product Value Calculators to find the answer, but that would have been unsatisfying. With a little trial-and-error, I found that blackboard also has a product value of 1,710,720:

blackboard = 2 × 12 × 1 × 3 × 11 × 2 × 15 × 1 × 18 × 4 = 1,710,720

There were three things about solving this problem that I really enjoyed:

1. My strategy involved substitutions: I replaced a letter or a pairs of letters by other pairs of letters that have the same product value. For instance, the t and c in Patrick could be replaced by o and d, because both pairs have a product value of 60.
2. Calculating the product values for Patrick and blackboard reveal two distinct factorizations for 1,710,720.
3. How cool is it that I’m a mathy folk, and my name and blackboard have the same product value?

(Incidentally, my boss David found that his name and the word chalk have the same product value. Some would argue that its numerological destiny that we work together and are friends.)

So now I’ll offer  the challenge to you. Can you find a word that has the same product value as your name? Good luck!

Of course, if that’s more thinking than you care to do right now, you could just access the product value calculator. But what fun would that be?